The $\kappa$-cookbook: a novel generalizing approach to unify $\kappa$-like distributions for plasma particle modeling

TL;DR

This paper introduces a comprehensive generalized $ppa$-distribution model that unifies various existing $ppa$-distributions used in plasma physics, providing analytical tools and highlighting their similarities and differences.

Contribution

A new generalized $ppa$-distribution framework that encompasses all known $ppa$-models, with analytical expressions and a comparison of their macroscopic parameters.

Findings

All $ppa$-distribution recipes yield similar macroscopic parameters.

The regularized $ppa$-distribution allows flexible parameterization without constraints.

Analytical expressions for moments, Debye length, and entropy are derived.

Abstract

In the literature different so-called $\kappa$-distribution functions are discussed to fit and model the velocity (or energy) distributions of solar wind species, pickup ions or magnetospheric particles. Here we introduce a generalized (isotropic) $\kappa$-distribution as a "cookbook", which admits as special cases, or "recipes", all the other known versions of $\kappa$-models. A detailed analysis of the generalized distribution function is performed, providing general analytical expressions for the velocity moments, Debye length, and entropy, and pointing out a series of general requirements that plasma distribution functions should satisfy. From a contrasting analysis of the recipes found in the literature, we show that all of them lead to almost the same macroscopic parameters with a small standard deviation between them. However, one of these recipes called the regularized $\kappa$-distribution provides a functional alternative for macroscopic parameterization without any constraint for the power-law exponent $\kappa$.